I live about 400 miles north of Anchorage, think about 150 miles south of the Arctic Circle...
the sun really does just circle the horizon here, and we currently have no darkness. It gets like its cloudy..for about two hours then the sun is coming up..
I have noticed the chickens go to roost about 9.00pm, the rooster then crows us up about 3am. he is the first up and the hens follow...
Mine lay their eggs during the day all year round....
In the winter they get 8 hours of artifical daylight when its at its darkest, in december dawn is a t 10.00am and dusk is at 2.00pm.
We had no heat this year either with the coldest winter on record for decades, reached -50 below and lower, and they had eggs right the way through...
They just get used to it like people they adapt to their environment, like any animal would. Their ciracdian rhythm tends to stay intact.